Kramer Eric M
Physics Department, Simon's Rock College, 84 Alford Road, Great Barrington, MA 01230, USA.
J Theor Biol. 2002 May 21;216(2):147-58. doi: 10.1006/jtbi.2002.2551.
The beautiful patterns apparent in wood grain have their origin in the alignment of fusiform initial cells in the vascular cambium of trees. We develop a mathematical model to describe the orientation of fusiform initial cells, and their interaction with the plant hormone indole-3-acetic acid (auxin). The model incorporates the following four assumptions: (1) auxin is actively transported parallel to the long axis of the initials, (2) auxin diffuses perpendicular to the long axis of the initials, (3) the initials tend to orient parallel to the flux of auxin through the cambium, and (4) adjacent initials tend to orient parallel to one another. Each assumption is justified on the basis of available evidence and cast in mathematical form. Our main result is a pair of nonlinear differential equations that describe the coupling between the distribution of auxin in the cambium and the orientation of fusiform initials. Numerical solutions to the equations show qualitative resemblance to the wood grain patterns observed at branch junctions, wounds and knots, and topological defects.
木材纹理中明显的美丽图案起源于树木维管形成层中纺锤状原始细胞的排列。我们开发了一个数学模型来描述纺锤状原始细胞的取向，以及它们与植物激素吲哚 - 3 - 乙酸（生长素）的相互作用。该模型包含以下四个假设：（1）生长素沿原始细胞的长轴方向进行主动运输；（2）生长素垂直于原始细胞的长轴方向扩散；（3）原始细胞倾向于沿生长素通过形成层的通量方向平行排列；（4）相邻的原始细胞倾向于彼此平行排列。每个假设都基于现有证据进行了论证，并以数学形式呈现。我们的主要成果是一对非线性微分方程，它们描述了形成层中生长素分布与纺锤状原始细胞取向之间的耦合关系。这些方程的数值解在定性上与在树枝分叉处、伤口和节疤处观察到的木材纹理图案以及拓扑缺陷相似。
